Definition df-singleton 34164

Description: Define the singleton function. See brsingle 34219 for its value. (Contributed by Scott Fenton, 4-Apr-2014.)

Assertion

Ref	Expression
df-singleton	⊢ Singleton = ((V × V) ∖ ran ((V ⊗ E ) △ ( I ⊗ V)))

Detailed syntax breakdown of Definition df-singleton

Step	Hyp	Ref	Expression
1		csingle 34140	. 2 class Singleton
2		cvv 3432	. . . 4 class V
3	2, 2	cxp 5587	. . 3 class (V × V)
4		cep 5494	. . . . . 6 class E
5	2, 4	ctxp 34132	. . . . 5 class (V ⊗ E )
6		cid 5488	. . . . . 6 class I
7	6, 2	ctxp 34132	. . . . 5 class ( I ⊗ V)
8	5, 7	csymdif 4175	. . . 4 class ((V ⊗ E ) △ ( I ⊗ V))
9	8	crn 5590	. . 3 class ran ((V ⊗ E ) △ ( I ⊗ V))
10	3, 9	cdif 3884	. 2 class ((V × V) ∖ ran ((V ⊗ E ) △ ( I ⊗ V)))
11	1, 10	wceq 1539	1 wff Singleton = ((V × V) ∖ ran ((V ⊗ E ) △ ( I ⊗ V)))

This definition is referenced by:  brsingle  34219  fnsingle  34221